Let A1 denote the first eigenvalue of Q(x) + Ax^20p(x) = 0, p(a) = (b) =...

 

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Let A1 denote the first eigenvalue of Q"(x) + Ax^20p(x) = 0, p(a) = (b) = 0 for some a, b > 0. Show that the nonlinear problem p"(x) + Ax^2p(x) - p(x)^3 = 0, p(a) = (b) = 0 (1) has only the zero solution provided that λ = A1. Let A1 denote the first eigenvalue of Q"(x) + Ax^20p(x) = 0, p(a) = (b) = 0 for some a, b > 0. Show that the nonlinear problem p"(x) + Ax^2p(x) - p(x)^3 = 0, p(a) = (b) = 0 (1) has only the zero solution provided that λ = A1.

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ANS WER Let 1 be the corresponding e igen function for A 1 Sin... View the full answer